Registered Data
Contents
- 1 [CT035]
- 1.1 [01147] A convergent numerical scheme to a McKendrick-von Foerster equation with diffusion
- 1.2 [00722] Scalar auxiliary variable schemes for Cahn-Hilliard systems with mass source
- 1.3 [00937] Asymptotic and numerical approaches to degeneracies in Stefan problems
- 1.4 [02483] Existence and uniqueness of traveling wave solutions for competition-diffusion systems
[CT035]
[01147] A convergent numerical scheme to a McKendrick-von Foerster equation with diffusion
- Session Date & Time : 5C (Aug.25, 13:20-15:00)
- Type : Contributed Talk
- Abstract : This talk presents a numerical scheme for a nonlinear McKendrick–von Foerster equation with diffusion in age (MV-D) with the Dirichlet boundary condition. The main idea for deriving the scheme is to use discretization based on the method of characteristics to the convection part, and the finite difference method to the rest of the terms. The nonlocal terms are dealt with the quadrature methods. As a result, an implicit scheme is obtained for the boundary value problem under consideration. The consistency and the convergence of the proposed numerical scheme are established. Moreover, numerical simulations are presented to validate the theoretical results.
- Classification : 35K20, 65N12, 92D25
- Author(s) :
- Suman Kumar Tumuluri (University of Hyderabad)
[00722] Scalar auxiliary variable schemes for Cahn-Hilliard systems with mass source
- Session Date & Time : 5C (Aug.25, 13:20-15:00)
- Type : Contributed Talk
- Abstract : The scalar auxiliary variable approach presents a novel way to discretize a large class of dissipative systems. We consider a general Cahn-Hilliard system with mass source that may not admit a known dissipative structure, and so the stability of discrete solutions is not immediate. With a bounded mass source, we show stability and convergence of time discrete solutions for a first-order scheme, and apply our ideas to systems in tumour growth, image inpainting and segmentation.
- Classification : 35K35, 35K55, 65M12, 65Z05
- Author(s) :
- Andrew Lam (Hong Kong Baptist University)
- Ru Wang (Hong Kong Baptist University)
[00937] Asymptotic and numerical approaches to degeneracies in Stefan problems
- Session Date & Time : 5C (Aug.25, 13:20-15:00)
- Type : Contributed Talk
- Abstract : This talk discusses how asymptotic analysis and numerics can be combined to devise computational schemes to moving boundary $($Stefan$)$ problems more accurately; in particular, this relates to degenerate situations where the solution domain is initially of zero extent, or where a domain that was initially present disappears completely. A further subtlety concerns whether a new domain starts to form instantaneously or after some delay time.
- Classification : 35K40, 35K65, 35K60
- Author(s) :
- Michael Vynnycky (University of Limerick)
- Sarah Mitchell (University of Limerick)
[02483] Existence and uniqueness of traveling wave solutions for competition-diffusion systems
- Session Date & Time : 5C (Aug.25, 13:20-15:00)
- Type : Contributed Talk
- Abstract : In this talk, we will consider the existence and uniqueness of traveling wave solutions for a class of competition-diffusion models. We find a necessary and sufficient condition for the existence of non-decreasing traveling wave solutions connecting trivial and positive equilibria. Moreover, with the help of the asymptotic behaviors of such solutions at positive infinity, we also prove that traveling wave solutions are unique up to translations.
- Classification : 35K40, 35K57, 35B35
- Author(s) :
- Jian-Jhong Lin (National Taipei University of Technology)